I have managed to copy kmail's mail form one system to another (But not my address book, or mail filters - I wish the kmail developers could fix this!)
First problem: Older versions of kmail kept mail in ~/Mail, newer versions keep mail in ~/.Mail. So make sure you are moving your mail to the correct directory!
Make sure your mail, once copied over, has the correct ownership (ie the new user on the new system).
I then deleted the *.index and *.index.ids files.
Then I started kmail. It was quite slow to start up, as it had to re-index several thousand emails, but then my mail was where it was supposed to be.